The paint used to make lines on roads must reflect enough li

The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let N denote the true average reflectometer reading for a new type of paint under consideration. A test of H_0 :mu = 20 versus H_a: mu > 20 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.) State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

Solution

a)
Null, H0: U=20
Alternate, H1: U>20
to =3.3
| to | =3.3
Critical Value
The Value of |t | with n-1 = 17 d.f is 1.74
We got |to| =3.3 & | t | =1.74
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho

Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

b)
to =1.6
| to | =1.6
Critical Value
The Value of |t | with n-1 = 9 d.f is 2.821
We got |to| =1.6 & | t | =2.821
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.

c)
to =-0.5
P-Value :Right Tail - Ha : ( P > -0.5 ) = 0.68898
Hence Value of P0.01 < 0.68898,Here We Do not Reject Ho

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.